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arXiv · 2305.06508

Dimensions of some LCD BCH codes

Hanglong Zhang·Xiwang Cao
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Abstract

In this paper, we investigate the first few largest coset leaders modulo $\frac{q^m+1}λ$ where $λ\mid q+1$ and $q$ is an odd prime power, and give the dimensions of some LCD BCH codes of length $\frac{q^m+1}λ$ with large designed distances.We also determine the dimensions of some LCD BCH codes of length $n=\frac{(q^m+1)}λ$ with designed distances $2\leq δ\leq \frac{ q^{\lfloor(m+1)/2\rfloor}}λ+1$, where $ λ\mid q+1$ and $1<λ<q+1$. The LCD BCH codes presented in this paper have a sharper lower bound on the minimum distance than the BCH bound.

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Hanglong Zhang, Xiwang Cao. 2023-05-11. Dimensions of some LCD BCH codes. https://arxiv.org/abs/2305.06508

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